I had read on Chowhound in a 2003 post that Puritan Bakery in Carson, CA supplies most notable SoCal burger chains (including InNOut, Fatburger, and Tommy's, among others) with their buns.
Interesting article in last week's Orange County Register about Puritan & their process:
From "The secret behind SoCal's best burgers" by Nancy Luna
Puritan buns are made the same way your grandmother used to bake bread in the kitchen – only at a much larger scale... Flour, water, shortening and yeast are mixed and set aside in a large trough where it rises and develops flavor...
At the end of the four- to six-hour fermentation process, the mixture (not considered dough, yet) bubbles up – becoming a taffy-like blob.
Plant workers and machines then take the sponge mixture and add sugar, yeast, salt, flour and water to make dough, which is then shaped into buns before baking. The end result of the seven-hour process is a spongy, pliable bun...
While its base sponge-dough recipe is the same, Puritan customizes buns for restaurants and chains with specific needs. For example, In-N-Out's four-inch buns are "tweaked" (Puritan won't say how) for better grilling results. Tommy's buns are made to better support its heavy chili slathered burgers. Islands restaurants use a larger, five-inch bun. Seeded buns are delivered to The Habit.
Full article at http://www.ocregister.com/articles/puritan-293345-burger-bakery.html
I think it's interesting that the sponge has shortening in it.... Haven't seen that before in a sponge, is it uncommon? Not to mention that their entire process (from sponge to finished product) is about 7 hours.
I also wonder about the "tweaks" for better grilling results; more sugar or shortening for better browning? Any other ideas of what tweaks they might be applying, for example, for support of heavier burgers?
I learned from the photos that Puritan does use hamburger bun pans. In the photo gallery, there is a decent photo showing the bun texture.